document.write( "Question 44138: Don't understand what is correct way to do this!\r
\n" ); document.write( "\n" ); document.write( "Question: What's wrong with using product rule for solving equation -4(under radical sign) times -4 (under the radical sign?\r
\n" ); document.write( "\n" ); document.write( "I would say put both under radical and then square to get correct answer of 4. Notes say what is correct product? Hinted that 4 was not it.\r
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Algebra.Com's Answer #29078 by psbhowmick(878) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28-4%29\"$ is not a real number. So the rule you mentioned is not applicable here.
\n" ); document.write( "Such numbers, with -ve sign under the radical, are called imaginery.
\n" ); document.write( " $\"sqrt%28-1%29\"$ is called as the imaginery square root of unity and is denoted by $\"i\"$ .
\n" ); document.write( "So, $\"i=sqrt%28-1%29\"$ .
\n" ); document.write( "Hence, $\"i%5E2+=+-1\"$ .
\n" ); document.write( "Now, $\"sqrt%28-4%29\"$ = $\"sqrt%284%2A%28-1%29%29\"$ = $\"sqrt%284%29%2Asqrt%28-1%29\"$ = $\"2i\"$ .
\n" ); document.write( "Hence, $\"sqrt%28-4%29%2Asqrt%28-4%29\"$ = $\"2i%2A2i\"$ = $\"4i%5E2\"$ = -4\r
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\n" ); document.write( "\n" ); document.write( "To know more about such problems read chapters on imaginery and complex numbers.
\n" ); document.write( "All the laws of Mathematical operation which hold for real numbers are not necessarily true with imaginery numbers. \n" ); document.write( "

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